Washington (CNN)Hillary Clinton's sizable lead among Democrats in New Hampshire has been trimmed to single digits as Vermont Sen. Bernie Sanders makes a strong push in a state that narrowly broke Clinton's way in 2008 to keep her campaign alive.

The poll marks a significant tightening of the contest since the May Granite State Poll, which included Elizabeth Warren on its list of candidates. In that poll, Clinton stood at 51%, with Warren at 20% and Sanders at 13%.

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Photos:Alternatives to Hillary Clinton 2016

Jim Webb: "I look forward to listening and talking with more people in the coming months as I decide whether or not to run."

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Joe Biden: "That's a family personal decision that I'm going to make sometime at the end of the summer."

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Martin O'Malley: "I've been very encouraged as I travel around the country by a number of people who repeat again and again and again their desire for getting things done again as a country and also for new leadership to get those things done."

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Elizabeth Warren: "I'm not running for president....I don't get who writes these headlines or what they're about. I think there's just kind of a pundit world out there."

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Jerry Brown: "If no one runs and [everyone] says we'll have an absent Democratic nominee, would I rule that out? I mean, that would be a little silly, wouldn't it?"

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Former Rhode Island Governor Lincoln Chafee is a one-time Republican, turned independent, now Democrat and is exploring a run for the presidency. On Hillary Clinton, he told CNN "... anybody who voted for the Iraq War should not be president and certainly should not be leading the Democratic Party."

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Bernie Sanders: "I haven't made up my final decision and I've got to say a lot of my strongest supporters say, 'Bernie, you've gotta stay out of the damn Democratic Party, run as an Independent."

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Kirsten Gillibrand: The New York senator has said she'll support Hillary Clinton "110 percent."

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Andrew Cuomo (in 2014): "I'm focusing on running for governor. And then I'm going to focus on being the best governor I can be."

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Brian Schweitzer: When asked by Time if he would be a better candidate for president than Clinton: "Well, I think so, of course. I think I have a background and a resume that isn't just in government."

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Several shifts in the poll seem to explain much of Sanders' gain. Looking at the demographic breakdown in primary preferences, men, younger voters and liberals appear to have moved broadly toward Sanders in the last month. Among men, 52% backed Clinton in the May survey, that fell to 32% in the new poll, while 47% now support Sanders. Likewise, among liberals, a 51% to 16% Clinton advantage is now a 48% to 41% Sanders edge. And among voters under age 50, Clinton has fallen from majority support to a near even split in the new poll, 37% back Clinton while 39% favor Sanders.

And likely Democratic primary voters are now more apt to see Sanders as the candidate who "best represents the values of Democrats like yourself." Sanders trounces Clinton, with 41% of Democratic primary voters saying Sanders does, to 30% who chose Clinton. In the May poll, 38% said Clinton was tops on this question, with 22% choosing Warren and just 13% picking Sanders.

Sanders has also gained dramatically in favorability ratings among Democrats since May. In the new poll, 66% say they have a favorable view of the Vermont senator, while just 11% hold an unfavorable view. In May, 45% had a favorable view and 11% held an unfavorable one.

And the Vermont Senator also holds a big edge over Clinton as the most empathetic candidate in the field; 45% say he's the one who cares the most about people like you, compared with 24% who pick Clinton on that score.

Clinton's advantages are apparent in voters' preferences on the issues, however. She is more trusted to handle two of the top domestic issues in the race: The economy (37%, compared with 28% who prefer Sanders' approach) and health care (43% Clinton to 27% Sanders).

And the former secretary of state's advantages are larger on matters of foreign affairs. She holds a wide lead as the more trusted candidate to handle both international trade policy (55% say they trust Clinton compared with Sanders' 14%; Biden is at 11% on that one) and terrorism (45% Clinton to 12% Biden and 11% Sanders).

But when it comes to dealing with "big banks and corporations," things are much tighter: 36% trust Sanders compared to 31% who favor Clinton.

More see Clinton as presidential than Sanders, with 38% saying she has the personal characteristics and qualities a president should have, compared with 27% who think Sanders is best representative of those qualities. Further, 56% of Democratic voters say she is the strongest leader in the field. On that question, just 13% say Sanders has the edge.

Still, 28% describe Clinton as the "least honest" candidate in the field. No other candidate is named by more than 5% of likely Democratic primary voters.

Photos:Bernie Sanders in the spotlight

Photos:Bernie Sanders in the spotlight

U.S. Sen. Bernie Sanders, an independent from Vermont, is the longest-serving independent in the history of Congress.

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Sanders, right, leads a sit-in organized by the Congress of Racial Equality in 1962. The demonstration was staged to oppose housing segregation at the University of Chicago. It was Chicago's first civil rights sit-in.

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Sanders takes the oath of office to become the mayor of Burlington, Vermont, in 1981. He ran as an independent and won the race by 10 votes.

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Sanders, right, tosses a baseball before a minor-league game in Vermont in 1984. U.S. Sen. Patrick Leahy, center, was also on hand.

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In 1987, Sanders and a group of Vermont musicians recorded a spoken-word folk album. "We Shall Overcome" was first released as a cassette that sold about 600 copies. When Sanders entered the U.S. presidential race in 2015, the album surged in online sales. But at a CNN town hall, Sanders said, "It's the worst album ever recorded."

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Sanders reads mail at his campaign office in Burlington in 1990. He was running for the U.S. House of Representatives after an unsuccessful bid in 1988.

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In 1990, Sanders defeated U.S. Rep. Peter Smith in the race for Vermont's lone House seat. He won by 16 percentage points.

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Sanders sits next to President Bill Clinton in 1993 before the Congressional Progressive Caucus held a meeting at the White House. Sanders co-founded the caucus in 1991 and served as its first chairman.

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Barack Obama, then a U.S. senator, endorses Sanders' Senate bid at a rally in Burlington in 2006.

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Sanders takes part in a swearing-in ceremony at the U.S. Capitol in January 2007. He won his Senate seat with 65% of the vote.

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Sanders chats with Dr. John Matthew, director of The Health Center in Plainfield, Vermont, in May 2007. Sanders was in Plainfield to celebrate a new source of federal funding for The Health Center.

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Sanders speaks to reporters in 2010 about the Obama administration's push to extend Bush-era tax cuts. Three days later, Sanders held a filibuster against the reinstatement of the tax cuts. His speech, which lasted more than eight hours, was published in book form in 2011. It is called "The Speech: A Historic Filibuster on Corporate Greed and the Decline of Our Middle Class."

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Sanders and U.S. Rep. Jeff Miller, chairman of the House Committee on Veterans' Affairs, walk to a news conference on Capitol Hill in 2014. Sanders was chairman of the Senate Committee on Veterans' Affairs.

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In March 2015, Sanders speaks in front of letters and petitions asking Congress to reject proposed cuts to Social Security and Medicare.

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In July 2015, two months after announcing he would be seeking the Democratic Party's nomination for President, Sanders spoke to nearly 10,000 supporters in Madison, Wisconsin. "Tonight we have made a little bit of history," he said. "You may know that some 25 candidates are running for President of the United States, but tonight we have more people at a meeting for a candidate for President of the United States than any other candidate has."

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Seconds after Sanders took the stage for a campaign rally in August 2015, a dozen protesters from Seattle's Black Lives Matter chapter jumped barricades and grabbed the microphone from the senator. Holding a banner that said "Smash Racism," two of the protesters -- Marissa Johnson, left, and Mara Jacqueline Willaford -- began to address the crowd.

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Sanders shakes hands with Hillary Clinton at a Democratic debate in Las Vegas on October 13. The hand shake came after Sanders' take on the Clinton email scandal. "Let me say something that may not be great politics, but the secretary is right -- and that is that the American people are sick and tired of hearing about the damn emails," Sanders said. "Enough of the emails, let's talk about the real issues facing the United States of America."

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Sanders embraces Remaz Abdelgader, a Muslim student, during an October 2015 event at George Mason University in Fairfax, Virginia. Asked what he would do about Islamophobia in the United States, Sanders said he was determined to fight racism and "build a nation in which we all stand together as one people."

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Sanders waves while walking in a Veterans Day parade in Lebanon, New Hampshire, in November 2015.

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Sanders sits with Killer Mike at the Busy Bee Cafe in Atlanta in November 2015. That evening, the rapper and activist introduced Sanders at a campaign event in the city. "I'm talking about a revolutionary," Killer Mike told supporters. "In my heart of hearts, I truly believe that Sen. Bernie Sanders is the right man to lead this country."

Sanders speaks at a campaign rally in Ann Arbor, Michigan, on March 7. Sanders won the state's primary the next day, an upset that delivered a sharp blow to Clinton's hopes of quickly securing the nomination.

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Sanders speaks at a campaign event in New York's Washington Square Park on April 13.

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Sanders speaks at a rally in Santa Monica, California, on June 7. He pledged to stay in the Democratic race even though Hillary Clinton secured the delegates she needed to become the presumptive nominee.

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Sanders endorses Democratic presidential nominee Hillary Clinton at a rally in Portsmouth, New Hampshire, on July 12.

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Sanders addresses delegates on the first day of the Democratic National Convention in Philadelphia, Pennsylvania, on July 25.

Clinton's favorability ratings remain strong and have generally held steady: 74% have a positive impression, 19% a negative one, about the same as in May.

O'Malley makes a small gain here, with his favorable rating climbing from 10% in May to 16% now. The former Maryland governor remains largely unknown, however, with 72% unable to offer an opinion.

One interesting contrast between the two parties in New Hampshire: while 75% of Republicans say they're still trying to make up their minds about who to support, that figure stands at 54% among Democrats, suggesting Democratic support is solidifying more quickly than Republican support.

The CNN/WMUR New Hampshire Primary Poll was conducted by telephone by the University of New Hampshire Survey Center from June 18-24 among 1,010 adult residents of New Hampshire. Of those, 360 said they plan to vote in the Democratic presidential primary. Results among likely Democratic primary voters have a margin of sampling error of plus or minus 5.2 percentage points.